Noé de Rancourt: On subspaces of certain Orlicz sequence spaces

Data: sexta-feira, 16 de dezembro de 2022, às 11h00.

Formato híbrido: Sala A249 IME (Presencial). Google meet:  meet.google.com/ijh-tzhe-snr

Palestrante: Noé de Rancourt (U. Lille)

Título:  On subspaces of certain Orlicz sequence spaces

Resumo:   Ferenczi and Rosendal conjectured two decades ago that every separable Banach space that is not isomorphic to a Hilbert space should have continuum-many pairwise non-isomorphic subspaces. After progress made by Cuellar Carrera, it only remains to prove it for near Hilbert spaces, that are, spaces whose geometric properties are very close to Hilbertspaces. In a common work with Ondřej Kurka, we proved that some Orlicz sequence spaces that are near Hilbert satisfy Ferenczi and Rosendal's conjecture. More precisely, we proved that Orlicz spaces associated with a regular enough Orlicz function which is "close" to t² should have asymptotically Hilbertian subspaces; such spaces have been proved by Anisca to have many subspaces. I will present the proof of our result, which involves a study of Banach-Mazur distances of finite-dimensional subspaces of Orlicz spaces to Hilbert spaces.

Adi Tcaciuc: Rank-one perturbations of quasinilpotent operators

Data: sexta-feira, 16 de dezembro de 2022, às 9h30.

Formato híbrido: Sala A249 IME (Presencial). Google meet:  meet.google.com/ijh-tzhe-snr

Palestrante: Adi Tcaciuc (MacEwan University)

Título:  Rank-one perturbations of quasinilpotent operators

Resumo:   The Invariant Subspace Problem (ISP) is one of the most famous problems in Operator Theory, and is concerned with the search of non-trivial, closed, invariant subspaces for bounded operators acting on a separable Banach space. Considerable success has been achieved over the years both for the existence of such subspaces for many classes of operators, as well as for non-existence of invariant subspaces for particular examples of operators. Quasinilpotent operators are the ones for which zero is the only value in the spectrum. While there are counterexamples to ISP for quasinilpotent operators on non-reflexive Banach spaces, the ISP for quasinilpotent operators is still open in the reflexive case. In this talk, I will present an approach to the ISP for quasinilpotent operators by examining the stability of the spectrum under rank-one perturbations.